Basic Semiconductors (intrinsic concentration)

Ok, so in an intrinsic semiconductor we know that the intrinsic concentration ([itex] n_i [/itex]) is roughly [itex] 10^10 cm^{-3} [/itex] at room temperature, and that [itex] n=p=n_i [/itex] under equilibrium conditions.

Now why is it that at zero temperature, (i.e. [itex] 0K [/itex]) does [itex] n_i [/itex] have any value? I know that that [itex] n_i [/itex] does have a temperature dependence, but why any value at 0K?

Also, another question. If an intrinsic semiconductor is in equilibrium it has no current correct (lack of diffusion)? So does an intrinsic semiconductor in equilibrium have any electrons in the conduction band?

What's confusing me are the "standard" diagrams (of extrinsic) semiconductors that show the energy levels of the conduction band, valence band, donor and acceptor energy levels. It shows that at 0K, there are no electrons in the conduction band (so wouldn't n=0 !!! ???; so how can np=ni^2), next the energy is increased and some electrons jump energy levels from the donor to the conduction band, etc...

I would appreciate any input here, I have a test on Tuesday... and I do not want to just be algebra crunching out the answers. I feel I'm missing something fundamental here. Thanks in advance.

I am not quite sure what you are asking, but I think what you are asking is why real materials do not quite behave as predicted by the bandgap model.

First of all, the intrinsic concentration is mainly just a property of the specfic crystal; for real materials such as Si it basically depends on the purity, number of defects etc.

Now, according to the bandgap model what happens when you raise the temperature is that once kbT is approximately equal to the gap energy you will start to populate the conduction band and the material becomes conducting.
Hence, if you cool e.g. Si below about 30-40K it becomes a good insulator regardless of the doping (unless it is VERY overdoped so that the conduction band is above the valence band). However, other properties (such as the loss tangent) can still be indirectly related to the intrinsic carrier concentration (high resistivity silicon has a lower loss than ordinary silicon even at very low temperatures); something I don't think you can explain within the framework of the simplest bandgap models.

Hence, there is a significant difference between theory and real materials here. There is no such thing as a "perfect" semiconductor since real materials always contain defects, impurites etc. This means that while e.g. Si is a good insulator at low temperatures; it is NOT a perfect insulator; phenomena like hopping conductivity etc are still present which leads to a finite resistance.

Thank you for the response. Actually, I was making a fundamental error.

I didn't understand how the intrinsic concentration could have a value greater than 0 when the temperature is equal to 0K.

In the text we are using, they have a plot of experimental values of the intrinsic concentration along with a table of "important" values. The leftmost column has temperature, while the rightmost has the intrinsic concentration. The first measurement at a temperature of zero has the concentration value of ~10^8 cm^-3.

Also, another question. If an intrinsic semiconductor is in equilibrium it has no current correct (lack of diffusion)? So does an intrinsic semiconductor in equilibrium have any electrons in the conduction band?

I think these 2 are quite independent right? It would be possible for there to be electrons in the conduction band (and holes in the valence band) at thermal equilibrium simply so long as there is no net current (density) resulting from their movement.